# Suboptimal cuts: Their enumeration, weight and number

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## Abstract

We present (1) an algorithm that enumerates the cuts of a network by increasing weight with polynomial delay, and (2) an algorithm that computes the *k*-th minimum weight in polynomial time for fixed *k* We also show that in the case of undirected networks there are only polynomially many cuts that have the *k*-th minimum weight for any fixed *k* (whereas directed networks can have exponentially many different minimum cuts).

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© Springer-Verlag Berlin Heidelberg 1992